Abstract Algebra Answers

vicky is thinking a number a number less than 700.when she interchanges ones and hundreds digit, the number increases by 297. when she interchanges the ones and tens digit, the result increases by 18.can you find the number she thinking of?

A softdrink cup is cylindrical in shape. I f its volume is 1884cm3 and the radius of the circular base is 10cm, how deep is the cup?

If A, B are subgroups of G such that b^(-1) Ab⊇A for any b ϵ B, show that AB≤G.

Prove that polynomial ring of 2 independent variables over field is not a PID.

Is Z[X] a PID ?

Prove that all ideals in field are trivial.

Prove that every ideal with invertible element inside is trivial ideal of a given ring.

Find quotient ring Z_4[x]/(x*x+1), and define its group of units.

Find quotient ring Q[x]/(x^4-10x*x+1), and find number field which it is isomorphic.

Find quotient ring Q[x]/(x*x-2), and find number field which it is isomorphic.